3Q6 philosophical transactions. [anno 1773. 



if the angle of the ecliptic and equator had not varied: but that distance was 

 found by actual obsei-vation to be 51*.6 less. By so much therefore must the 

 obliquity of the ecliptic have become less in an interval of 82 years ; and conse- 

 quently the variation in 100 years will be 62". Q2. If the observations of Arctu- 

 rus be reduced to the solstice of ]77l> and the zenith distance of the sun's 

 centre, as observed in that year, be made use of in the same manner, the vari- 

 ation of the obliquity in 81 years will be found = 48".8, and in 100 years = 60'. 

 If the quantity of the arc of Mr. Flamsteed's instrument were accurately 

 known, the observations which he made at the winter solstice in 169O might be 

 compared with later observations, in order to determine both the quantity of the 

 obliquity in 169O, and also the variation since his time. Accordingly, Mr. H. 

 endeavoured to determine the error of the arc of the instrument between 28° and 

 75° of zenith distance, and proceeded in the following manner. He computed 

 several observations of the stars ^ Tauri, n Pleiadum, n and ju Geminorum, and 

 ^, 0-, and Sagittarii, as observed by Mr. Flamsteed in the years l6go, 1691, 

 and 1692, and reducing them to the years 1760 and 1766; he compared the 

 differences of declination between those stars, resulting from Mr. Flamsteed's 

 observations, with the differences given by the places of the same stars, as settled 

 by Dr. Bradley in 1760, and also by actual observations of the same stars made 

 at Shirburn castle in 1766; and by combining these differences together, he 

 found that the whole arc of 90° was too short by 43". Supposing the error to be 

 uniform, the proportional part of this quantity, thus found for the solstitial 

 zenith distance of the sun in June = 13".4, is nearly confirmed on the authority 

 of Mr. Flamsteed himself, who, in the prolegomena to the 3d volume of the 

 Historia Coelestis, where he is deducing the latitude of the Royal Observatory at 

 Greenwich, and the quantity of the obliquity in 1690, from his own observations, 

 allows the zenith distances at 28°, 36", and 40°, on his instrument, to be too 

 small by 15" and by 20", at 76°. Mr. H. therefore computed the observations 

 of the sun, made from November 30 to December 20 of 1 690, which, reduced 

 to the solstice, are as in the following table; to which are subjoined the obser- 

 vations made by himself at Oxford, at the winter solstice of 177 1. 



Of the former, the mean is 7+" i8' 25.9" Of the latter, the mean is 75° 13' 17.3" 



Error of the line of collimation . . — 1 10 Sun's parallax — 8.5 



7+ 57 15.9 75 13 8,8 



Sun's parallax —8.5 Nutation -{-7.9 



Ti 57 7.4 75 13 16.7 



Nutation —9-6 Error of the line of collimation . . + 4-.8 



Mean solstitial zenith distance of Mean solstitial zenith dist. of the 



the Sun's centre, Dec. itpo ..7+ 56" 57 8 sun's centre, December 1 77 1 75 13 21.5 



The mean obliquity of the ecliptic resulting from the zenith distances, as 

 observed at the two solstices in 1690, by applying the known latitude of the 



